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Integer matrix that does not belong to a free group of rank 2

I'm given two matrices in $SL_2(\mathbb{Z})$ $$ A = \left(\begin{array}{cc} 2 & 3\\ 3 & 5 \end{array}\right), \ \ B = \left(\begin{array}{cc} 5 & 3\\ 3 & 2 \end{ …
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